1. Field of the Invention
The present invention relates in general to a method and an apparatus for lapping teeth of a pair of gears, and more particularly, to such lapping method and apparatus which permit lapping of the gears so as to reduce an error of the gears which occurred during fabrication of the gears.
2. Discussion of the Prior Art
Lapping is a conventional process for finishing the tooth surfaces of a pair of gears which are used in mesh with each other. An example of such a gear lapping process is disclosed in Publication No. 1-97520 of unexamined Japanese Patent Application, in which one of a pair of gears is positively driven at a predetermined speed, in mesh with the other gear, in the presence of a suitable abrasive lapping compound or powder between the gears, while a braking torque is applied to the above-indicated other gear, so that the surfaces of the gear teeth are lapped with the lapping powder, for improved smoothness of the tooth surfaces.
However, the conventional lapping process as described above suffers from a drawback where one or both of the two gears has/have considerable geometrical or dimensional errors such as eccentricity of the pitch circle with respect to the axis of the gears, which are caused during fabrication or generation of the gears. Namely, the amount of an error of the gear or gears after the finish lapping operation may be larger than that before the finish lapping.
For example, the degree of eccentricity (eccentricity error) of a gear is reflected by the maximum cumulative pitch error of the gear or gears. A test showed an increase of the maximum cumulative pitch error after the finish lapping of a specimen gear, as compared with that before the finish lapping, as indicated by the graph of Fig. 7. The maximum cumulative pitch error was obtained as a difference between the maximum and minimum values of a cumulative pitch error which is a sum of individual pitch errors between the adjacent ones of the successive gear teeth. As the individual pitch errors are either a positive or a negative value, the cumulative pitch error changes in the circumferential direction of the gear. The increase in the maximum cumulative pitch error means an increase in the eccentricity error of the gear by the lapping operation.
As indicated above, a braking torque is applied to one (hereinafter referred to as "braked gear") of the two gears during a lapping operation with the gears rotated in mesh with each other. The increase in the eccentricity error of the lapped gear is considered to be caused by a change in the overall lapping torque of the braked gear, which change takes place due to the eccentricity error of the braked gear or the other gear before the lapping. The overall lapping torque of the brake gear is a sum of the braking torque TB, and an inertial torque based on the moment of inertia of the braked gear. In the conventional lapping method, the braking torque TB is held constant, but the inertial torque varies as the gears are rotated. The inertial torque is equal to (Ig.multidot..alpha.G), where IG represents the moment of inertia, while .alpha.G represents the angular acceleration value. Since the angular acceleration value .alpha.G is at a minimum when the eccentricity error amount is at a maximum, and it is at a maximum when the eccentricity error amount is at a minimum, the inertial torque varies during rotation of the braked gear.
When the overall lapping torque is at a minimum with the maximum eccentricity error amount, the surface pressure of the contacting teeth of the meshing two gears is not enough for a sufficient amount of metal removal or lapping depth to correct or reduce the eccentricity error of, the gear or gears. When the overall lapping torque is at a maximum with the minimum eccentricity error amount, on the other hand, the surface pressure of the contacting gear teeth is excessive for an adequate amount of metal removal by the lapping. In the conventional lapping method, therefore, the change in the overall lapping torque during a lapping operation of the gears does not meet the change in the eccentricity error amount so as to assure an adequate control of the metal removal for reducing or eliminating the eccentricity of the gears. In other words, the gear teeth that should be lapped by a larger amount are lapped by a smaller amount, than the gear teeth that should be lapped by a smaller amount, whereby the maximum cumulative pitch error of the gears after the lapping tends to be larger than that before the lapping.
Similar drawbacks may be encountered due to a change in the overall lapping torque which arises from a dimensional or geometrical error of the gears other than the eccentricity error.